Mutual Orbital Inclinations Between Cold Jupiters and Inner Super-Earths

TL;DR

This study investigates the orbital plane alignments between cold Jupiters and inner super-Earths, finding they are generally coplanar with some variation, and that higher multiplicity inner systems tend to be more aligned with outer giants.

Contribution

It provides the first statistical constraint on the mutual inclination distribution between cold Jupiters and inner super-Earths using Kepler and Doppler data.

Findings

Mutual inclinations are generally low, with a Rayleigh scale parameter around 11.8 degrees.

Systems with higher inner transit multiplicity show lower mutual inclinations.

Cold Jupiters tend to be more coplanar with inner systems than previously assumed.

Abstract

Previous analyses of Doppler and Kepler data have found that Sun-like stars hosting "cold Jupiters" (giant planets with $a\gtrsim 1\,\mathrm{AU}$) almost always host "inner super-Earths" (1-$4\,R_\oplus$, $a\lesssim1\,\mathrm{AU}$). Here, we attempt to determine the degree of alignment between the orbital planes of the cold Jupiters and the inner super-Earths. The key observational input is the fraction of Kepler stars with transiting super-Earths that also have transiting cold Jupiters. This fraction depends on both the probability for cold Jupiters to occur in such systems, and on the mutual orbital inclinations. Since the probability of occurrence has already been measured in Doppler surveys, we can use the data to constrain the dispersion of the mutual inclination distribution. We find $\sigma=11.8^{+12.7}_{-5.5}\,\mathrm{deg}$ (68% confidence) and $\sigma>3.5\,\mathrm{deg}$ (95% confidence), where $\sigma$ is the scale parameter of the Rayleigh distribution. This suggests that planetary orbits in systems with cold Jupiters tend to be coplanar - although not quite as coplanar as those in the Solar System, which have a mean inclination from the invariable plane of $1.8\,\mathrm{deg}$. We also find evidence that cold Jupiters have lower mutual inclinations relative to inner systems with higher transit multiplicity. This suggests a link between the dynamical excitation in the inner and outer systems. For example, perturbations from misaligned cold Jupiters may dynamically heat or destabilize systems of inner super-Earths.